Generalized dualities had an intriguing incursion into Double Field Theory (DFT) in terms of local $O(d,d)$ transformations. We review this idea and use the higher derivative formulation of DFT to compute the first order corrections to generalized dualities. Our main result is a unified expression that can be easily specified to any generalized T-duality (Abelian, non-Abelian, Poisson-Lie, etc.) or deformations such as Yang-Baxter, in any of the theories captured by the bi-parametric deformation (bosonic, heterotic strings and HSZ theory), in any supergravity scheme related by field redefinitions. The prescription allows further extensions to higher orders. As a check we recover some previously known particular examples.
Poisson-Lie duality is a generalization of abelian and non-abelian T-duality, and it can be viewed as a map between solutions of the low-energy effective equations of string theory, i.e. at the (super)gravity level. We show that this fact extends to the next order in $α'$ (two loops in $σ$-model perturbation theory) provided that the map is corrected. The $α'$-correction to the map is induced by the anomalous Lorentz transformations of the fields that are necessary to go from a doubled $O(D,D)$-covariant formulation to the usual (super)gravity description.
We generalize the Giveon-Kutasov duality by adding possible Chern-Simons interactions for the $U(N)$ gauge group. Some of the generalized dualities are known in the literature and many others are new to the best of our knowledge. The dualities are connected to the non-supersymmetric bosonization duality via mass deformations. For $N=1$, there are an infinite number of magnetic-dual theories.
The worldsheet theories that describe Poisson-Lie T-dualisable $σ$-models on group manifolds as well as integrable $η$, $λ$ and $β$-deformations provide examples of ${\cal E}$-models. Here we show how such ${\cal E}$-models can be given an elegant target space description within Double Field Theory by specifying explicitly generalised frame fields forming an algebra under the generalised Lie derivative. With this framework we can extract simple criteria for the R/R fields and the dilaton that extend the ${\cal E}$-model conditions to type II backgrounds. In particular this gives conditions for…
In this note we have compared two different perturbation techniques that could be used to generate solutions of Einstein's equations in presence of negative cosmological constant. One of these two methods is derivative expansion and the other is an expansion in inverse powers of dimension. Both the techniques generate space-time with a singularity shielded by a dynamical event horizon. We have shown that in the appropriate regime of parameter space and with appropriate choice of coordinates, the metrics and corresponding horizon dynamics, generated by these two different techniques, are exactl…
We determine the complete spacetime action to first order in $α'$ for the massless fields of bosonic string theory compactified on a $d$-dimensional torus. A fully systematic procedure is developed that brings the action into a minimal form in which all fields apart from the metric enter only with first-order derivatives. T-duality implies that this action must have a global $\mathrm{O}(d,d,\mathbb{R})$ symmetry, and we show that this requires a Green-Schwarz type mechanism for $α'$-deformed $\mathrm{O}(d,d,\mathbb{R})$ transformations. In terms of a frame formalism with ${\rm GL}(d)\times {\r…
In this note, we have compared two different perturbation techniques that are used to generate dynamical black-brane solutions to Einstein equation in presence of negative cosmological constant. One is the `derivative expansion', where the gravity solutions are in one-to-one correspondence with the solutions of relativistic Navier-Stokes equation. The second is the expansion in terms of inverse power of space-time dimensions and here the gravity solutions are dual to a co-dimension one dynamical membrane, embedded in AdS space and coupled to a velocity field. We have shown that in large number…
We survey physical models which capture the main concepts of double field theory on para-Hermitian manifolds. We show that the geometric theory of Lagrangian and Hamiltonian dynamical systems is an instance of para-Kahler geometry which extends to a natural example of a Born geometry. The corresponding phase space geometry belongs to the family of natural almost para-Kahler structures which we construct explicitly as deformations of the canonical para-Kahler structure by non-linear connections. We extend this framework to a class of non-Lagrangian dynamical systems which naturally encodes the …
This contribution is based on a talk given by the author at the "Dualities and Generalized Geometries" session of the Corfu Summer Institute 2018 workshops. We overview the results of [1], focusing our attention on integrable $λ$-deformations of WZW models with boundaries.
Generalized $2$-split for higher-derivative YM and GR amplitudes at tree-level
Beijing Computational Science Research Center（北京计算科学研究中心）；Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University（扬州大学物理科学与技术学院引力与宇宙学中心）
In literature one can find many generalizations of the usual Leibniz derivative, such as Jackson derivative, Tsallis derivative and Hausdorff derivative. In this article we present a connection between Jackson derivative and recently proposed Hausdorff derivative. On one hand, the Hausdorff derivative has been previously associated with non-extensivity in systems presenting fractal aspects. On the other hand, the Jackson derivative has a solid mathematical basis because it is the $\overline{q}$-analog of the ordinary derivative and it also arises in quantum calculus. From a quantum deformed $\…
